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<h1>trexp2</h1><p><span class="helptopic">matrix exponential for so(2) and se(2)</span></p><h2>SO(2)</h2>
<p>
<strong>R</strong> = <span style="color:red">trexp2</span>(<strong>omega</strong>) is the matrix exponential (2x2) of the so(2) element <strong>omega</strong> that
yields a rotation matrix (2x2).

</p>
<p>
<strong>R</strong> = <span style="color:red">trexp2</span>(<strong>theta</strong>) as above, but rotation by <strong>theta</strong> (1x1).

</p>
<h2>SE(2)</h2>
<p>
<strong>T</strong> = <span style="color:red">trexp2</span>(<strong>sigma</strong>) is the matrix exponential (3x3) of the se(2) element
<strong>sigma</strong> that yields a homogeneous transformation  matrix (3x3).

</p>
<p>
<strong>T</strong> = <span style="color:red">trexp2</span>(<strong>tw</strong>) as above, but the se(2) value is expressed as a vector <strong>tw</strong>
(1x3).

</p>
<p>
<strong>T</strong> = <span style="color:red">trexp2</span>(<strong>sigma</strong>, <strong>theta</strong>) as above, but se(2) rotation of <strong>sigma</strong>*<strong>theta</strong>, the
rotation part of <strong>sigma</strong> (3x3) must be unit norm.

</p>
<p>
<strong>T</strong> = <span style="color:red">trexp</span>(<strong>tw</strong>, <strong>theta</strong>) as above, but se(2) rotation of <strong>tw</strong>*<strong>theta</strong>, the
rotation part of <strong>tw</strong> must be unit norm.

</p>
<h2>Notes</h2>
<ul>
  <li>Efficient closed-form solution of the matrix exponential for arguments that are
so(2) or se(2).</li>
  <li>If theta is given then the first argument must be a unit vector or a
skew-symmetric matrix from a unit vector.</li>
</ul>
<h2>References</h2>
<ul>
  <li>Robotics, Vision & Control: Second Edition, Chap 2,
P. Corke, Springer 2016.</li>
  <li>"Mechanics, planning and control"
Park & Lynch, Cambridge, 2017.</li>
</ul>
<h2>See also</h2>
<p>
<a href="trexp.html">trexp</a>, <a href="skew.html">skew</a>, <a href="skewa.html">skewa</a>, <a href="Twist.html">Twist</a></p>
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<p class="copy">&copy; 1990-2014 Peter Corke.</p>
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